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While Koopman-based techniques like extended Dynamic Mode Decomposition arenowadays ubiquitous in the data-driven approximation of dynamical systems,quantitative error estimates were only recently established. To this end, bothsources of error resulting from a finite dictionary and only finitely-many datapoints in the generation of the surrogate model have to be taken into account.We generalize the rigorous analysis of the approximation error to the controlsetting while simultaneously reducing the impact of the curse of dimensionalityby using a recently proposed bilinear approach. In particular, we establishuniform bounds on the approximation error of state-dependent quantities likeconstraints or a performance index enabling data-based optimal and predictivecontrol with guarantees.

Towards reliable data-based optimal and predictive control using extended DMD